MHT CET · Physics · Oscillations
A block of mass ' \(\mathrm{M}\) ' rests on a piston executing S.H.M. of period one second. The amplitude of oscillations, so that the mass is separated from the piston, is
(acceleration due to gravity, \(\mathrm{g}=10 \mathrm{~ms}^{-2}, \pi^2=10\) )
- A 0.25 m
- B 0.5 m
- C 1 m
- D \(\infty\)
Answer & Solution
Correct Answer
(A) 0.25 m
Step-by-step Solution
Detailed explanation
Given that, \(\mathrm{T}=2 \pi \sqrt{\frac{\mathrm{m}}{\mathrm{k}}}=1 \mathrm{~s}\)
\(\therefore \quad \frac{\mathrm{m}}{\mathrm{k}}=\frac{1}{4 \pi^2}\)
The block will separate, when the restoring force exceeds the force due to gravity. i.e., \(\mathrm{kx} \geq \mathrm{Mg}\)
\(\therefore \quad \mathrm{x} \geq \frac{\mathrm{Mg}}{\mathrm{k}}=\frac{\mathrm{g}}{4 \pi^2}=\frac{10}{4 \times 10}=0.25 \mathrm{~m}\)
\(\therefore \quad \frac{\mathrm{m}}{\mathrm{k}}=\frac{1}{4 \pi^2}\)
The block will separate, when the restoring force exceeds the force due to gravity. i.e., \(\mathrm{kx} \geq \mathrm{Mg}\)
\(\therefore \quad \mathrm{x} \geq \frac{\mathrm{Mg}}{\mathrm{k}}=\frac{\mathrm{g}}{4 \pi^2}=\frac{10}{4 \times 10}=0.25 \mathrm{~m}\)
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